The chain rule states that the derivative of f (g (x)) is f' (g (x))⋅g' (x). In other words, it helps us differentiate *composite functions*. For example, sin (x²) is a composite function because it …

The chain rule tells us how to find the derivative of a composite function. Brush up on your knowledge of composite functions, and learn how to apply the chain rule correctly.

Through a worked example, we explore the Chain rule with a table. Using specific x-values for functions f and g, and their derivatives, we collaboratively evaluate the derivative of a …

The chain rule tells us how to find the derivative of a composite function. This is an exceptionally useful rule, as it opens up a whole world of functions (and equations!) we can now differentiate.

We also emphasize the importance of fully applying the Chain Rule, and avoid the pitfall of taking the derivative of the outer function with respect to the derivative of the inner function.

The chain rule tells us how to find the derivative of a composite function. This is an exceptionally useful rule, as it opens up a whole world of functions (and equations!) we can now differentiate.

If you don't understand implicit differentiation, you'll probably struggle with the chain rule and related rates, which is arguably the most important part of derivatives.

Now let's tackle a worked example of composite functions, using the example f (x) = cos³ (x). By applying the chain rule, we differentiate this function, breaking it down into its components x³ …

Let's explore the process of determining the second derivative of y with respect to x from an implicit equation. Using implicit differentiation, we apply the chain rule and quotient rule. This …

The Fundamental Theorem of Calculus tells us how to find the derivative of the integral from 𝘢 to 𝘹 of a certain function. But what if instead of 𝘹 we have a function of 𝘹, for example sin (𝘹)? Then we …